Recently a paper was published by AQR where the authors advocate for an integrated approach to multi-factor portfolios, preferring securities that exhibit strong characteristics across all desired factors instead of a mixed approach, where securities are selected based upon extreme exposure to a single characteristic.
We believe the integrated approach fails to acknowledge the impact of the varying lengths over which different factors mature, ultimately leading to a portfolio more heavily influenced by higher turnover factors.
The Importance of Factor Maturity Cliff Asness, founder of AQR, recently published a paper titled My Factor Philippic. This paper was written in response to the recently popularized article How Can “Smart Beta” Go Horribly Wrong? which was co-authored by Robert Arnott, co-founder of Research Affiliates.
Arnott argues that many popular factors are currently historically overvalued and, furthermore, that the historical excess return offered by some recently popularized factors can be entirely explained by rising valuation trends in the last 30 years. Caveat emptor, warns Arnott: valuations always matter.
Much to our delight (after all, who doesn’t like to see two titans of industry go at it?), Asness disagrees.
One of the primary arguments laid out by Asness is that valuation is a meaningless predictor for factors with high turnover.
The intuition behind this argument is simple: while valuations may be a decent predictor of forward annualized returns for broad markets over the next 5-to-10 years, the approach only works because the basket of securities stays mostly constant. For example, valuations for U.S. equities may be a good predictor because we expect the vast majority of the basket of U.S. equities to stay constant over the next 5-to-10 years.
The same is not true for many factors. For example, let’s consider a high turnover factor like momentum.
Valuations of a momentum basket today are a poor predictor of annualized returns of a momentum strategy over the next 5-to-10 years because the basket of securities held could be 100% different three months from now.
Unless the same securities are held in the basket, valuation headwinds or tailwinds will not necessarily be realized.
For the same reason, valuation is also poor as an explanatory variable of factor returns. Asness argues that Arnott’s warning of valuation being the secret driver of factor returns is unwarranted in high turnover factors.
The paper attempts to conclude the current debate about the best way to build multi-factor portfolios. The first approach is to mix, where a portfolio is built by combining stand-alone factor portfolios. The second approach is to integrate, where a portfolio is built by selecting securities that have simultaneously strong exposure to multiple factors at once.
A figure from the paper does a good job of illustrating the difference. Below, a hypothetical set of stocks is plotted based upon their current valuation and momentum characteristics.
In the top left, a portfolio of deep value stocks is selected. In the top right, the mix approach is demonstrated, where the deepest value and the highest momentum stocks are selected.
In the bottom left, the integrated approach is demonstrated, where the securities simultaneously exhibiting strong valuation and momentum characteristics are selected.
Finally, in the bottom right we can see how these two approaches differ: with yellow securities being those only found in the mix portfolio and blue securities being found only in the integrated portfolio.
It is worth noting that the ETF industry has yet to make up its mind on the right approach.
GlobalX and Goldman Sachs prefer the mix approach in their ETFs (SCIU / GSLC) while JPMorgan and iShares prefer the integrate approach (JPUS / LRGF).
The argument made by those taking the integrated approach is that they are looking for securities with well-rounded exposures rather than those with extreme singular exposures. Integrators argue that this approach helps them avoid holding securities that might cancel each other out. If we look back towards the mix example above (top right), we can see that many securities selected due to strength in one factor are actually quite poor in the other.
Integrators claim that this inefficiency can create a drag in the mix portfolio. Why hold something with strong momentum if it has a very poor valuation score that is only going to offset it?
We find it somewhat ironic that FFPS and Asness both publish for AQR, because we would argue that Asness’s argument points out the fundamental flaw in the theory outlined by integrators. Namely: the horizons over which the premia mature differ.
Therefore, a strong positive loading in a factor like momentum is not necessarily offset by a strong negative loading in a factor like value. Furthermore, by integrating we run the risk of the highest turnover factor actually dominating the integrated selection process.
Data In the rest of this commentary, we will be using industry data from the Kenneth French data library. For momentum scores, we calculate 12 one-month total return and calculate cross-sector z-scores[1]. For valuation scores, we calculate a normalized 5-year dividend yield score and then calculate cross-sector z-scores.[2]
Do Factor Premia Actually Mature at Different Time Periods? In his paper, Asness referenced the turnover of a factor portfolio as an important variable. We prefer to think of high turnover factors as factors whose premium matures more quickly.
For example, if we buy a stock because it has high relative momentum, our expectation is that we will likely hold it for longer than a day, but likely much shorter than a year. Therefore, a strategy built off relative momentum will likely have high turnover because the premium matures quickly.
On the other hand, if we buy a value stock, our expectation is that we will have to hold it for up to several years for valuations to adequately reverse. This means that the value premium takes longer to mature – and the strategy will likely have lower turnover.
We can see this difference in action by looking at how valuation and momentum scores change over time.
We see similar pictures for other industries. Yet, looks can be deceiving and the human brain is excellent at finding patterns where there are none (especially when we want to see those patterns). Can we actually quantify this difference?
One way is to try to build a model that incorporates both the randomness of movement and how fast these scores mean-revert. Fitting our data to this model would tell us about how quickly each premium matures.
One such model is called an Ornstein-Uhlenbeck process (“OU process”). An OU process follows the following stochastic differential equation:
To translate this into English using an example: the change in value z-score from one period to the next can be estimated as a “magnetism” back to fair value plus some randomness. In the equation, theta tells us how strong this magnetism is, mu tells us what fair value is, and sigma tells us how much influence the randomness has.
For our momentum and valuation z-scores, we would expect mu to be near-zero, as over the long-run we would not expect a given sector to exhibit significantly more or less relative momentum or relative cheapness/richness than peer sectors.
Given that we also believe that the momentum premium is realized over a shorter horizon, we would also expect that theta – the strength of the magnetism, also called the speed of mean reversion – will be higher. Since that strength of magnetism is higher, we will also need sigma – the influence of randomness – to be larger to overcome it.
So how to the numbers play out?[3]
For the momentum z-scores:
Theta
Mu
Sigma
NoDur
0.97
0.02
1.00
Durbl
1.00
0.03
1.63
Manuf
1.22
-0.03
0.96
Enrgy
0.98
0.06
1.69
HiTec
1.04
0.03
1.49
Telcm
1.15
-0.07
1.52
Shops
1.22
0.03
1.24
Hlth
0.84
0.11
1.39
Utils
1.48
-0.09
1.61
Other
1.18
-0.09
1.13
Average
1.10
0.00
1.36
For the valuation z-scores:
Theta
Mu
Sigma
NoDur
0.11
-0.20
0.34
Durbl
0.08
0.58
0.49
Manuf
0.13
0.01
0.37
Enrgy
0.07
0.19
0.40
HiTec
0.09
0.23
0.33
Telcm
0.07
0.03
0.38
Shops
0.11
-0.15
0.36
Hlth
0.05
-0.47
0.36
Utils
0.06
-0.35
0.40
Other
0.11
-0.01
0.37
Average
0.08
-0.01
0.38
We can see results that echo our expectations: the speed of mean-reversion is significantly lower for value than momentum. In fact, the average theta is less than 1/10th.
The math behind an OU-process also lets us calculate the half-life of the mean-reversion, allowing us to translate the speed of mean reversion to a more interpretable measure: time.
The half-life for momentum z-scores is 0.27 years, or about 3.28 months. The half-life for valuation z-scores is 3.76 years, or about 45 months. These values more or less line up with our intuition about turnover in momentum versus value portfolios: we expect to hold momentum stocks for a few months but value stocks for a few years.
Another way to analyze this data is by looking at how long the relative ranking of a given industry group stays consistent in its valuation or momentum metric. Based upon our data, we find that valuation ranks stayed constant for an average of approximately 120 trading days, while the average length of time an industry group held a consistent momentum rank was only just over 50 days.
Maturity’s Influence on Integration The scatter plots drawn by FFPS are deceiving because they only show a single point in time. What they fail to show is how the locations of the dots change over time.
With the expectation that momentum scores will change more rapidly than valuation scores, we would expect to see points move more rapidly up and down along the Y-axis than we would see them move left and right along the X-axis. Given this, our hypothesis is that changes in our inclusion score are driven more significantly by changes in our momentum score.
To explore this, we create an integration score, which is simply the sum of the valuation and momentum z-scores. Those industries in the top 30% of integration scores at any time are held by the integrated portfolio.
To distill the overall impact of momentum score changes versus valuation score changes, we need to examine the absolute value of these changes. For example, if the momentum score change was +0.5 and the valuation score change was -0.5, the overall integration score change is 0. Both momentum and value, in this case, contributed equally (or, contributed 50% each), to the overall score change.
So a simple formula for measuring the relative percentage contribution to score change is:
If value and momentum score changes contributed equally, we would expect the average contribution to equal 50%.
The average contribution based upon our analysis is 72.18% (with a standard error of 0.24%). The interquartile range is 59.02% to 91.19% and the median value is 79.47%.
Put simply: momentum score changes are a much more significant contributor to integration score changes than valuation score changes are.
We find that this effect is increased when we examine only periods when an industry is added or deleted from the integrated portfolio. In these periods, the average contribution climbs to 78.46% (with a standard error of 0.69%), with an interquartile range of 70.28% to 94.46% and a median value of 85.57%.
Changes in the momentum score contribute much more significantly than value score changes.
Integration: More Screen than Tilt? The objective of the integrated portfolio approach is to find securities with the best blend of characteristics.
In reality, because one set of characteristics changes much more slowly, certain securities can be sidelined for prolonged periods of time.
Let’s consider a simplified example. Every year, the 10 industry groups are assigned a random, but unique, value score between 1 and 10.
Similarly, every month, the 10 industry groups are assigned a random, but unique, momentum score between 1 and 10.
The integration score for each industry group is calculated as the sum of these two scores. Each month, the top 3 scoring industry groups are held in the integrated portfolio.
What is the probability of an industry group being in the integrated portfolio, in any given month, if it has a value score of 1? What about 2? What about 10? Numerical simulation gives us the following probabilities:
So if these are the probabilities of an industry group being selected in a given month given a certain value score, what is the probability of an industry group not being selected into the integrated portfolio at all during the year it has a given value score?
If an industry group starts the year with a value score of 1, there is 99.1% probability it will never being selected into the integrated portfolio all year.
Conclusion While we believe this topic deserves a significantly deeper dive (one which we plan to perform over the coming months), we believe the cursory analysis highlights a very important point: an integrated approach runs a significant risk of being more heavily influenced by higher turnover factors. While FFPS believe there are first order benefits to the integrated approach, we think the jury is still out and that those first order effects may actually be simply due to an increased exposure to higher turnover factors. Until more a more substantial understanding of the integrated approach is established, we continue to believe that a mixed approach is prudent. After all, if we don’t understand how a portfolio is built and the source of the returns it generates, how can we expect to manage risk?
[1] Z-scoring standardizes, on a relative basis, what would otherwise be arbitrary values.
[2] We use yield versus historical as our measure for valuation as a matter of convenience. However, there are two theoretical arguments justifying this choice. First, the most common measure of value is book-to-market (B/M), which assumes that fair valuation of a company is its book value. Another such model is the dividend discount model. If we assume a constant growth rate of dividends and a constant cost of capital for the company, then book value should be proportional to total dividends, or, equivalently, book-to-market proportional to dividend yield. Similarly, if you assume a constant long-term payout ratio, dividends per share are proportional to earnings per share, which makes yield inversely proportional to price-to-earnings, a popular valuation ratio.
[3] We used maximum likelihood estimation to calculate these figures.
In a commentary a few weeks ago entitled Growth Is Not “Not Value,” we discussed a problem in the index construction industry in which growth and value are often treated as polar opposites. This treatment can lead to unexpected portfolio holdings in growth and value portfolios. Specifically, we may end up tilting more toward shrinking, expensive companies in both growth and value indices.
The picture of what we want for each index looks more like this:
The overlap is not a bad thing; it simply acknowledges that a company can be cheap and growing, arguably a very good set of characteristics.
A common way of combining growth and value scores into a single metric is to divide growth ranks by value ranks. As we showed in the previous commentary, many index providers do something similar to this.
Essentially this means that low growth gets lumped in with high value and vice versa.
But how much does this affect the index allocations? Maybe there just are not many companies that get included or excluded based on this process.
Let’s play index provider for a moment.
Using data from Morningstar and Yahoo! Finance at the end of 2015, we can construct growth and value scores for each company in the S&P 500 and see where they fall in the growth/value planes shown above.
To calculate the scores, we will use an approach similar to the one in last commentary where the composite growth score is the average of the normalized scores for EPS growth, sales growth, and ROA, and the composite value score is the average of the normalized scores for P/B, P/S, and P/E ratios.
The chart below shows the classification when we take an independent approach to selecting growth and value companies based on those in the top third of the ranks.
In each class, 87% of the companies were identified as only being growth or value while 13% of companies were included in both growth and value.
The next chart shows the classifications when we use the ratio of growth to value ranks as a composite score and again select the top third.
Relative to what we saw previously, growth and value now extend further into the non-value (expensive) and non-value (cheap) realms of the graph, respectively.
There is also no overlap between the two categories, but we are now missing 16% of the companies that we had identified as good growth or value candidates before. On the flip side, 16% of the companies we now include were not identified as growth or value previously in our independent sort.
If we trust our independent growth and value ranking methodologies, the combined growth and value metric leaves out over a third of the companies that were classified as both growth and value. These companies did not appear in either index under the combined scoring scheme.
With the level of diversification in some of these indices, a few companies may not make or break the performance, but leaving out the top ones defeats the purpose of our initial ranking system. As with the NCAA March Madness tournament (won by Corey with a second place finish by Justin), having a high seed may not guarantee superior performance, but it is often a good predictor (since 1979, the champion has only been lower than a 3 seed 5 times).
Based on this analysis, we can borrow the final warning to buyers from the previous commentary:
“when you’re buying value and growth products tracking any of these indices, you’re probably not getting what you expect – or likely want.”
… and say that the words “probably” and “likely” are definitely an understatement for those seeking the best growth and value companies based on this ranking.
Growth and value have intuitive definitions, but there are many ways to quantify each.
As with broad factors, such as value, momentum, and dividend growth, the specific metrics used to describe growth and value may fall in and out of favor, depending on the market environment.
Taking a diversified approach to quantifying value and growth can lead to more consistent performance over time.
In our commentary a few weeks ago, we pointed out a key flaw that many index providers have in their growth and value style indices. The industry norm lumps “low value” in with “growth” and “low growth” in with “value” when, in reality, growth and value are independent characteristics of companies. The result is that many of the growth and value ETFs that track these indices are not giving investors what they expect – or what they want.
Final index construction aside, let’s go down to a more fundamental level: what are growth and value in the first place, and how do we measure them?
Intuitively, growth refers to companies that are growing and expected to continue, and value refers to companies that are currently cheap relative to their fair price.
Simple enough.
But a quick survey of index providers finds that the characteristics they use to measure a stock’s growth and value characteristics vary across the board:
Only one metric on each list is common to all four index providers (Sales per share growth trend for growth and book-to-price ratio for value).
So who is right?
We can test the performance of many of these metrics using data readily available online. The forward-looking growth data are more difficult to find historically, but general financial statement data is available on Morningstar’s website.
To keep matters simple, we will look at three metrics for each of growth and value. For growth: 3-year EPS growth, 3-year sales per share growth, and ROA. For value: the P/E, P/S, and P/B ratios.
And to keep things as realistic as possible, we will evaluate the stocks in the S&P 500 as they stood at the end of 2014. Relative to the current set of companies in the S&P 500, we added back in some companies that dropped out of the S&P 500 (mainly energy and materials companies) in 2015. Some mergers and acquisitions also make getting data for the companies more difficult. For example, Covidien was bought by Medtronic, AT&T bought DirecTV, and Kraft merged with Heinz. Since we will be focusing on relative performance differences rather than on absolute ones, we will simply reconstruct a proxy S&P 500 index using the data that is available. In all, our universe contains 481 companies.
Using the fundamental data from December 2014, we can sort based on each metric and select the top 160 companies (about one-third of the universe) and see how that “value” or “growth” portfolio would have performed in 2015. Within each portfolio, we equally weight for simplicity. Results are compared to an equal-weight benchmark to control for any out or underperformance arising from the equal-weight allocation methodology as opposed to stock selection.
There is significant variation during the year depending on which metric was used.
Source: Data from Yahoo! Finance and Morningstar, calculations by Newfound
Source: Data from Yahoo! Finance and Morningstar, calculations by Newfound
For growth, all of the portfolios tracked each other until mid-March when the portfolio formed on sales growth began to diverge. The portfolios formed on EPS growth and ROA continued to track each other until mid-June. At this time, ROA rallied hard, eclipsing the sales growth portfolio in the 4th quarter of 2015.
On the value front, the P/S ratio led through most of the year before falling back to the pack in the Fall. The P/E and P/B portfolios ended the year in very similar places, with the P/S portfolio eking out a ~65bp benefit over the other two portfolios.
Which Metric to Choose
One year is hardly enough data to make a sound judgment as to which metric is the best for selecting growth and value stocks. As we have said many times before, even though we may know a factor (e.g. value) has outperformed in the past and is likely to do so in the future based on behavioral evidence, stating whether that factor will outperform in any given year is tough.
Likewise, deciding which measure of a factor will outperform in a given year is also difficult. Even with value companies, a metric like P/E ratio may not work well when companies with strong sales experience short-term earnings shocks or when companies are able to inflate earnings based on accounting allowances. The P/B ratio may not work well in periods when service oriented companies, which rely on intangible human capital as a large driver of growth, are being rewarded in the market.
Let’s take a closer look at some popular ways of quantifying the value factor.
“Value”, as it stands in academic literature, is commonly measured using the P/B ratio. This is what the famous Fama-French Three Factor Model uses as its basis for calculating the value factor, high-minus-low (HML).
However, using data from Kenneth French going back to 1951, we can see that, for long-only portfolios, those formed both on P/E and P/S actually beat the portfolio formed on P/B both on an absolute and risk-adjusted basis.
Furthermore, AQR showed in their 2014 paper, “The Devil in HML’s Details,” that not only does the metric matter, but the method of calculating the metric matters, as well. While Fama and French calculated HML using book value data that was lagged by 6 months to ensure that data would be available, they also lagged price data by the same amount. The AQR paper proposed using the most recent price data for calculating P/B ratios and showed that their method was superior to the standard lagged-price method because using more current price data better captures the relationship between value and momentum.
The P/S and P/E ratios used in the table above are also calculated using lagged price data. Based on AQR’s research, we expect that those results might also be improved by using the current price data.
Different Measures of Factors May Ebb and Flow
We should be careful not to rush to judgment though. The fact that P/B has underperformed the other value metrics does not mean we should drop it entirely. It is helpful to remember that individual factors can go through periods of significant underperformance. The same is true for different ways of measuring a single factor. For example, over rolling 12-month periods, the return difference between portfolios formed portfolio on P/B, P/S, and P/E – all “value” metrics – has often been in excess of 2000bp!
Put bluntly: your mileage may vary dramatically depending on which value metric you choose.
Source: Data from Kenneth French Data Library, calculations by Newfound
With our 2015 example, we saw that P/S resulted in the best performing portfolio, but as we said before, different measures tend to cycle unpredictably. We can see which ones have been in favor historically by comparing each individual portfolio to the average of all three portfolios.
Source: Data from Kenneth French Data Library, calculations by Newfound
The fact that many index providers combine multiple metrics into a composite growth or value score is an acknowledgement of this unpredictability.
Averaging the different value portfolios would have led to a fraction of outperforming periods on par with the best individual portfolios, higher average outperformance than the P/S portfolio, and lower average underperformance than all three individual portfolios.
Source: Data from Kenneth French Data Library, calculations by Newfound
If you read our previous commentary about multi-factor portfolio construction, you’ll notice that the averaging we did above is approach #1 (the “or” method). In effect, we are investing in companies that have either low P/S, P/B, or P/E ratios. One way to implement this would be to form portfolios based on each metric and then average the allocations into a final value portfolio.
In practice, most index providers score companies based on each selected metric, normalize the scores, and then average them (sometimes using different weightings). The portfolio is then formed using this composite score. This is more in line with approach #2 from the commentary (the “and” approach), which favors companies that have some degree of combined strength across multiple metrics.
While we used value and momentum in the commentary to illustrate why using the “and” approach is problematic in multi-factor portfolios, using this approach isn’t as bad when attempting to identify a single factor. The problem with value and momentum stemmed from the difference in time that each factor took to mature. Using the “and” approach introduced drag from the shorter maturity factor.
If there is no convincing argument that an individual growth or value measure takes longer to mature than another (for instance, does P/S normalize faster than P/B), then taking the “and” approach is not likely to result in a worse outcome. In this case, where we are simply trying to identify growth or value, we care more about the predictive nature of each metric that goes into forming the portfolio.
The index providers vary considerably in regards to what characteristics they look at and how they weight them to arrive at a final portfolio. If you believe that the P/B ratio is the best determinant of company value then you will get the purest exposure with Russell. If you think return on assets is an important contributing factor to company growth, CRSP’s index will be more in line with your view.
However, if you are like us and concede that while there are many ways to quantify growth and value, no one method can outperform over every single period, a diversified approach may be your best option.
Style boxes give us the impression that “growth” and “value” sit at opposite ends of the spectrum.
In reality, whether a company is growing or shrinking (“growth”) is independent of whether a security is cheap or expensive (“value”).
To align with the single axis expectation of “growth versus value,” most index providers combine a growth score and a value score together to create a composite score, which is projected upon the “growth / value” spectrum.
In doing so, most value indices are laden with cheap, shrinking companies and most growth indices focus on expensive, growing ones. Neither truly represents a value or growth approach to investing.
Multi-Factor: Mix or Integrate?
By Corey Hoffstein
On July 11, 2016
In Portfolio Construction, Risk & Style Premia, Weekly Commentary
This blog post is available as a PDF here.
Summary
The Importance of Factor Maturity
Cliff Asness, founder of AQR, recently published a paper titled My Factor Philippic. This paper was written in response to the recently popularized article How Can “Smart Beta” Go Horribly Wrong? which was co-authored by Robert Arnott, co-founder of Research Affiliates.
Arnott argues that many popular factors are currently historically overvalued and, furthermore, that the historical excess return offered by some recently popularized factors can be entirely explained by rising valuation trends in the last 30 years.
Caveat emptor, warns Arnott: valuations always matter.
Much to our delight (after all, who doesn’t like to see two titans of industry go at it?), Asness disagrees.
One of the primary arguments laid out by Asness is that valuation is a meaningless predictor for factors with high turnover.
The intuition behind this argument is simple: while valuations may be a decent predictor of forward annualized returns for broad markets over the next 5-to-10 years, the approach only works because the basket of securities stays mostly constant. For example, valuations for U.S. equities may be a good predictor because we expect the vast majority of the basket of U.S. equities to stay constant over the next 5-to-10 years.
The same is not true for many factors. For example, let’s consider a high turnover factor like momentum.
Valuations of a momentum basket today are a poor predictor of annualized returns of a momentum strategy over the next 5-to-10 years because the basket of securities held could be 100% different three months from now.
Unless the same securities are held in the basket, valuation headwinds or tailwinds will not necessarily be realized.
For the same reason, valuation is also poor as an explanatory variable of factor returns. Asness argues that Arnott’s warning of valuation being the secret driver of factor returns is unwarranted in high turnover factors.
Multi-Factor: Mix or Integrate?
On July 2nd, Fitzgibbons, Friedman, Pomorski, and Serban (FFPS) – again from AQR – published a paper titled Long-Only Style Investing: Don’t Just Mix, Integrate.
The paper attempts to conclude the current debate about the best way to build multi-factor portfolios. The first approach is to mix, where a portfolio is built by combining stand-alone factor portfolios. The second approach is to integrate, where a portfolio is built by selecting securities that have simultaneously strong exposure to multiple factors at once.
A figure from the paper does a good job of illustrating the difference. Below, a hypothetical set of stocks is plotted based upon their current valuation and momentum characteristics.
In the top left, a portfolio of deep value stocks is selected. In the top right, the mix approach is demonstrated, where the deepest value and the highest momentum stocks are selected.
In the bottom left, the integrated approach is demonstrated, where the securities simultaneously exhibiting strong valuation and momentum characteristics are selected.
Finally, in the bottom right we can see how these two approaches differ: with yellow securities being those only found in the mix portfolio and blue securities being found only in the integrated portfolio.
It is worth noting that the ETF industry has yet to make up its mind on the right approach.
GlobalX and Goldman Sachs prefer the mix approach in their ETFs (SCIU / GSLC) while JPMorgan and iShares prefer the integrate approach (JPUS / LRGF).
The argument made by those taking the integrated approach is that they are looking for securities with well-rounded exposures rather than those with extreme singular exposures. Integrators argue that this approach helps them avoid holding securities that might cancel each other out. If we look back towards the mix example above (top right), we can see that many securities selected due to strength in one factor are actually quite poor in the other.
Integrators claim that this inefficiency can create a drag in the mix portfolio. Why hold something with strong momentum if it has a very poor valuation score that is only going to offset it?
We find it somewhat ironic that FFPS and Asness both publish for AQR, because we would argue that Asness’s argument points out the fundamental flaw in the theory outlined by integrators. Namely: the horizons over which the premia mature differ.
Therefore, a strong positive loading in a factor like momentum is not necessarily offset by a strong negative loading in a factor like value. Furthermore, by integrating we run the risk of the highest turnover factor actually dominating the integrated selection process.
Data
In the rest of this commentary, we will be using industry data from the Kenneth French data library. For momentum scores, we calculate 12 one-month total return and calculate cross-sector z-scores[1]. For valuation scores, we calculate a normalized 5-year dividend yield score and then calculate cross-sector z-scores.[2]
Do Factor Premia Actually Mature at Different Time Periods?
In his paper, Asness referenced the turnover of a factor portfolio as an important variable. We prefer to think of high turnover factors as factors whose premium matures more quickly.
For example, if we buy a stock because it has high relative momentum, our expectation is that we will likely hold it for longer than a day, but likely much shorter than a year. Therefore, a strategy built off relative momentum will likely have high turnover because the premium matures quickly.
On the other hand, if we buy a value stock, our expectation is that we will have to hold it for up to several years for valuations to adequately reverse. This means that the value premium takes longer to mature – and the strategy will likely have lower turnover.
We can see this difference in action by looking at how valuation and momentum scores change over time.
We see similar pictures for other industries. Yet, looks can be deceiving and the human brain is excellent at finding patterns where there are none (especially when we want to see those patterns). Can we actually quantify this difference?
One way is to try to build a model that incorporates both the randomness of movement and how fast these scores mean-revert. Fitting our data to this model would tell us about how quickly each premium matures.
One such model is called an Ornstein-Uhlenbeck process (“OU process”). An OU process follows the following stochastic differential equation:
To translate this into English using an example: the change in value z-score from one period to the next can be estimated as a “magnetism” back to fair value plus some randomness. In the equation, theta tells us how strong this magnetism is, mu tells us what fair value is, and sigma tells us how much influence the randomness has.
For our momentum and valuation z-scores, we would expect mu to be near-zero, as over the long-run we would not expect a given sector to exhibit significantly more or less relative momentum or relative cheapness/richness than peer sectors.
Given that we also believe that the momentum premium is realized over a shorter horizon, we would also expect that theta – the strength of the magnetism, also called the speed of mean reversion – will be higher. Since that strength of magnetism is higher, we will also need sigma – the influence of randomness – to be larger to overcome it.
So how to the numbers play out?[3]
For the momentum z-scores:
For the valuation z-scores:
We can see results that echo our expectations: the speed of mean-reversion is significantly lower for value than momentum. In fact, the average theta is less than 1/10th.
The math behind an OU-process also lets us calculate the half-life of the mean-reversion, allowing us to translate the speed of mean reversion to a more interpretable measure: time.
The half-life for momentum z-scores is 0.27 years, or about 3.28 months. The half-life for valuation z-scores is 3.76 years, or about 45 months. These values more or less line up with our intuition about turnover in momentum versus value portfolios: we expect to hold momentum stocks for a few months but value stocks for a few years.
Another way to analyze this data is by looking at how long the relative ranking of a given industry group stays consistent in its valuation or momentum metric. Based upon our data, we find that valuation ranks stayed constant for an average of approximately 120 trading days, while the average length of time an industry group held a consistent momentum rank was only just over 50 days.
Maturity’s Influence on Integration
The scatter plots drawn by FFPS are deceiving because they only show a single point in time. What they fail to show is how the locations of the dots change over time.
With the expectation that momentum scores will change more rapidly than valuation scores, we would expect to see points move more rapidly up and down along the Y-axis than we would see them move left and right along the X-axis.
Given this, our hypothesis is that changes in our inclusion score are driven more significantly by changes in our momentum score.
To explore this, we create an integration score, which is simply the sum of the valuation and momentum z-scores. Those industries in the top 30% of integration scores at any time are held by the integrated portfolio.
To distill the overall impact of momentum score changes versus valuation score changes, we need to examine the absolute value of these changes. For example, if the momentum score change was +0.5 and the valuation score change was -0.5, the overall integration score change is 0. Both momentum and value, in this case, contributed equally (or, contributed 50% each), to the overall score change.
So a simple formula for measuring the relative percentage contribution to score change is:
If value and momentum score changes contributed equally, we would expect the average contribution to equal 50%.
The average contribution based upon our analysis is 72.18% (with a standard error of 0.24%). The interquartile range is 59.02% to 91.19% and the median value is 79.47%.
Put simply: momentum score changes are a much more significant contributor to integration score changes than valuation score changes are.
We find that this effect is increased when we examine only periods when an industry is added or deleted from the integrated portfolio. In these periods, the average contribution climbs to 78.46% (with a standard error of 0.69%), with an interquartile range of 70.28% to 94.46% and a median value of 85.57%.
Changes in the momentum score contribute much more significantly than value score changes.
Integration: More Screen than Tilt?
The objective of the integrated portfolio approach is to find securities with the best blend of characteristics.
In reality, because one set of characteristics changes much more slowly, certain securities can be sidelined for prolonged periods of time.
Let’s consider a simplified example. Every year, the 10 industry groups are assigned a random, but unique, value score between 1 and 10.
Similarly, every month, the 10 industry groups are assigned a random, but unique, momentum score between 1 and 10.
The integration score for each industry group is calculated as the sum of these two scores. Each month, the top 3 scoring industry groups are held in the integrated portfolio.
What is the probability of an industry group being in the integrated portfolio, in any given month, if it has a value score of 1? What about 2? What about 10?
Numerical simulation gives us the following probabilities:
So if these are the probabilities of an industry group being selected in a given month given a certain value score, what is the probability of an industry group not being selected into the integrated portfolio at all during the year it has a given value score?
If an industry group starts the year with a value score of 1, there is 99.1% probability it will never being selected into the integrated portfolio all year.
Conclusion
While we believe this topic deserves a significantly deeper dive (one which we plan to perform over the coming months), we believe the cursory analysis highlights a very important point: an integrated approach runs a significant risk of being more heavily influenced by higher turnover factors. While FFPS believe there are first order benefits to the integrated approach, we think the jury is still out and that those first order effects may actually be simply due to an increased exposure to higher turnover factors. Until more a more substantial understanding of the integrated approach is established, we continue to believe that a mixed approach is prudent. After all, if we don’t understand how a portfolio is built and the source of the returns it generates, how can we expect to manage risk?